
THE
FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

Held at the University of Ottawa
Room B005 KED Building, 585 King Edward (map)

Organizers:
Vladimir Chernousov (Alberta) and Kirill Zainoulline
(Ottawa)
Local organizer committee: Caroline Junkins, Kirill
Zainoulline


OVERVIEW
In the last 1015 years the theory of linear algebraic groups has witnessed
an intrusion of the cohomological methods of modern algebraic geometry and
algebraic topology. These new methods have led to breakthroughs on a number
of classical problems in algebra, which are beyond the reach of earlier purely
algebraic techniques. The workshop will focus at the following new emerging
techniques and applications:
 The proof of the GrothendieckSerre conjecture based on the theory of affine
Grassmannians.
The GrothendieckSerre conjecture stated in 60's says that any rationally
trivial Gbundle is locally trivial (in Zariski topology), where G is a smooth
reductive group scheme over a local regular ring. In a recent preprint (Nov.
2012) Fedorov and Panin proved the conjecture in the geometric case using
new connections with the theory of affine Grassmannians.
 Computation of generalized equivariant cohomology of projective homogeneous
and toric varieties.
The notion of an algebraic oriented cohomology theory was introduced and extensively
studied during the last decade by Levine, Morel, Panin, Smirnov and others.
The universal such theory called algebraic cobordism has many applications
in the theory of quadratic forms and homogeneous spaces. Its equivariant version
is believed to contain all the information concerning cohomological behaviour
of homogeneous spaces. In particular, its computation can lead to a better
understanding of cohomology and related combinatorics of toric varieties.
OUTLINE OF THE PROGRAM
The workshop will run for three full days and a morning session during the
fourth day (Friday morning  Monday noon) and will feature a unique combination
of two introductory minicourses and researchlevel talks. The two minicourses
will have three 80 min. lectures each and directed towards PhD students and
young researchers. The topics are the following.
(a) Toric varieties and equivariant cohomology by Kalle Karu, University of
British Columbia
 The course will be an introduction to toric varieties and equivariant cohomology.
(b) Introduction to principal homogeneous spaces by Roman Fedorov, Kansas
State University
 The course will be devoted to the basics in the theory of torsors and the
GrothendieckSerre conjecture.
Besides the two minicourses, there will be invited onehour talks by the
leading experts in the area, as well as short talks by young researchers,
postdocs and graduate students.
INVITED SPEAKERS
Alex Duncan, University of Michigan
Stefan Gille, University of Alberta
Nikita Karpenko, University of Alberta
Daniel Krashen, University of Georgia
Nicole Lemire, Western University
Alexander Merkurjev, University of California at LosAngeles
Julia Pevtsova, University of Washington
Andrei Rapinchuk, University of Virginia
Zinovy Reichstein, University of British Columbia
Friday,
May 23 
9:0010:20 
Course I  Roman Fedorov (Kansas State)
Introduction to principal homogeneous spaces 
10:2010:40 
Coffee 
10:4012:00 
Course II  Kalle Karu (UBC)
Toric varieties and equivariant cohomology 
12:0013:30 
Lunch 
13:3014:20 
Alexander Merkurjev (UCLA)
Motivic decomposition of of certain group varieties 
14:3015:20 
Zinovy Reichstein (UBC)
An invariant of a representation of a finite group 
15:3016:20 
Andrei Rapinchuk (University of Virginia)
On algebraic groups with the same tori (joint work with V. Chernousov
and I. Rapinchuk) 
16:3016:55 
Igor Rapinchuk (Harvard University)
The genus of a division algebra 
17:0017:25 
Alexander Neshitov (Steklov Institute/Ottawa)
Invariants of degree 3 and torsion on Chow group of a versal flag. 
Saturday, May
24 
9:0010:20 
Course II  Kalle Karu (UBC)
Toric varieties and equivariant cohomology 
10:2010:40 
Coffee 
10:4012:00 
Course I  Roman Fedorov (Kansas State)
Introduction to principal homogeneous spaces 
12:0013:30 
Lunch 
13:3014:20 
Nikita Karpenko (Alberta)
Incompressibility of Weil transfer of generalized SeveriBrauer varieties

14:3015:20 
Julia Pevtsova (University of Washington)
Supports and tensor ideals for finite group schemes. 
15:3015:55 
Mathieu Huruguen (UBC)
Special reductive groups over an arbitrary field 
Sunday, May 25


Free morning 
13:3014:50 
Course I  Roman Fedorov (Kansas State)
Introduction to principal homogeneous spaces 
15:00 16:20 
Course II  Kalle Karu (UBC)
Toric varieties and equivariant cohomology 
16:3016:55 
Uladzimir Yahorau (Alberta)
Conjugacy theorem for extended affine Lie algebras 
17:0017:25 
Changlong Zhong (Alberta)
Equivariant cohomology and formal Demazure algebra 
17:3017:55 
Wanshun Wong (Ottawa)
Formal group rings of toric varieties 
Monday, May 26

9:009:50 
Nicole Lemire (Western)
Fourdimensional algebraic tori 
9:5010:10 
Coffee 
10:1011:00 
Daniel Krashen
TBA 
11:1012:00 
Alexander Duncan (Michigan)
Twisted Forms of Toric Varieties 
12:1013:00 
Stefan Gille (Alberta)
Geometrically rational surfaces with 0dimensional motives 
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Participants may also be interested in a closely related event, the 73rd
Algebra Day on May 27, 2014, at the University of Ottawa.
(organizer: Hadi Salmasian, room B005, KED)
9:30 Siddhartha Sahi (Rutgers University)
TBA
11:00 Arturo Pianzola (University of Alberta)
Nonabelian cohomology and infinite dimensional Lie theory (suite)
14:00 Michel Waldschmidt (Université Paris VI)
Three algebras arising from Multiple Zeta Values
Confirmed Participants as of May 12th
Full Name 
University/Affiliation 
Bardestani, Mohammad 
University of Ottawa 
Bose, Anirban 
Indian Statistical Institute 
Bumagin, Inna 
Carleton University 
Chernousov, Vladimir 
University of Alberta 
Christie, Aaron 
University of Ottawa 
Duncan, Alexander 
University of Michigan 
Fedorov, Roman 
Max Planck Institute Bonn 
Gille, Stefan 
University of Alberta 
Huruguen, Mathieu 
UBC 
Junkins, Caroline 
University of Ottawa 
Karpenko, Nikita 
University of Alberta 
Karu, Kalle 
University of British Columbia 
Krashen, Daniel 
University of Georgia 
Leclerc, MarcAntoine 
University of Ottawa 
Lemay, Joel 
University of Ottawa 
Lemire, Nicole 
Western University 
Lemire, Nicole 
Western University 
Lu, Haoye 
University of Ottawa 
Merkurjev, Alexander 
University of California, Los Angeles 
Neher, Erhard 
University of Ottawa 
Neshitov, Alexander 
University of Ottawa 
Nevins, Monica 
University of Ottawa 
Pevtsova, Julia 
University of Washington 
Pianzola, Arturo 
University of Alberta 
Polak, Jason 
McGill University 
Rapinchuk, Andrei 
University of Virginia 
Rapinchuk, Igor 
Harvard University 
Reichstein, Zinovy 
University of British Columbia 
Salmasian, Hadi 
University of Ottawa 
Sarkar, Soumen 
University of Regina 
Savage, Alistair 
University of Ottawa 
Wong, Wanshun 
University of Ottawa 
Yahorau, Uladzimir 
University of Alberta 
Zainoulline, Kirill 
University of Ottawa 
Zhong, Changlong 
University of Alberta 
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